The Belgium international's representative has revealed that his client is ready to move to a bigger club and added that he would be open to a transfer to the Spanish giants
The 20-year-old has already netted four goals and provided three assists in nine Ligue 1 appearances so far this season.
And Bico feels that Hazard has shown he has what it takes to succeed at the Santiago Bernabeu.
"He has shown right from the start of this campaign that he can play for any of the big clubs, including Real Madrid," the Belgian's agent was quoted as saying by Marca.
"It is clear to see that he has matured a lot recently and he looks ready to take the next step in his career.
"It's true that Real Madrid have been watching him for quite a while. I don't think that [Zinedine] Zidane's presence will necessarily be the decisive factor. Zidane has always praised him but that, on its own, will not be sufficient."
Hazard has a contract with Lille until the summer of 2015.